The Generalized Backward Differentiation methods for solving stiff higher-order ordinary differential equations are described. The convergence, zero stability and consistency of these methods are defined. Next, the zero stability and consistency conditions necessary for convergence are proven. The order for which the methods are zero stable is also determined.

in this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $e=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...

In this paper, we describe a decompositional approach to convergence proofs for stochastic hybrid systems given as probabilistic hybrid automata. We focus on a concept called “stability in probability,” which implies convergence of almost all trajectories of the stochastic hybrid system to a designated equilibrium point. By adapting classical Lyapunov function results to the stochastic hybrid c...

There has been much interest over the past decade in the problem of asymptotic stabilization of the angular velocity of a rigid body with only two torque inputs. The smooth feedback laws proposed in the literature provide asymptotic stability with nonexponential convergence rates. This paper proposes discontinuous feedback laws to achieve asymptotic stability with exponential convergence rates.

similarity between cultures, languages and arts is natural. literary genres are also related to each other. it is obvious that if literary works are to be concerned with a subject or particular theme, this convergence will be further and clearer. the sacred defense literature, which is a spiritual literature, came to the fore both in poetry and prose more than other literary types. due to its c...

Abstract. The purpose of this article is to survey some intrinsic methods for studying the stability of the nonlinear filter. By ‘intrinsic’ we mean methods which directly exploit the fundamental representation of the filter as a conditional expectation through classical probabilistic techniques such as change of measure, martingale convergence, coupling, etc. Beside their conceptual appeal and...

The problems of exponential stability and exponential convergence rate for a class of impulsive cellular neural networks with time-varying delays are studied. By means of the Lyapunov stability theory and discrete-time Halanay-type inequality technique, stability criteria for ensuring global exponential stability of noimpulsive discrete-time cellular neural networks and impulsive discrete-time ...